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Abstract argumentation is a reasoning model for evaluating arguments based on various semantics. SCC-recursiveness is a sophisticated property of semantics that provides a general schema for characterizing semantics through the decomposition along strongly connected components (SCCs). While this property has been extensively explored in various qualitative frameworks, it has been relatively neglected in quantitative argumentation. To fill this gap, we demonstrate that this property is well-suited to fuzzy extension semantics, which is a quantitative generalization of classical semantics in fuzzy argumentation frameworks (FAF). We tailor the SCC-recursive schema to enable the characterization of fuzzy extension semantics through the recursive decomposition of an FAF along its SCCs. Our contributions are twofold. Theoretically, we show that SCC-recursiveness provides an alternative approach to characterize fuzzy extension semantics, offering a deep understanding and better insight into these semantics. Practically, our schema provides a sound and complete algorithm for computing fuzzy extension semantics, which naturally reduces computational efforts when dealing with a large number of SCCs.